Noise removal, detection of abrupt changes and compression are studied via an unusual approach of signal analysis and representation. Differential algebra, noncommutative algebra and operational calculus lead to quite efficient and simple identification methods for signals and systems, which may be stationary or not. We thus obtain real time estimators which 1) yield excellent approximations of the signal derivatives, 2) are robust with respect to a large variety of noises without any necessity of knowing their statistical properties, 3) depend on explicit algebraic formulae.